Rough Correlations: Meta‐Analysis of Roughness Measures in Gravel Bed Rivers

Bed roughness height (k) is a key parameter for velocity prediction in open‐channel flows. There is not yet a firm consensus about whether characteristic particle size D84 or σz (standard deviation of the channel thalweg) better describes k in gravel bed streams. A data set of 1,788 flume and 713 field measurements with a wide range of channel morphologies and flow conditions were compiled to test whether D84 or σz is a better descriptor of k and to explore the influence of several controls on flow resistance variation. Tests were performed using four well‐known flow resistance equations. The results consistently show that σz outperforms D84 in predicting velocity and the Smart and Jäggi equation, with σz as k, outperforms other equations. The data set was grouped based on R/k (R is the hydraulic radius), channel morphologies, and study sites. σz performs better than D84 as a measure of k in all morphologies and much better for channels with large instream wood. The analysis shows R/k is a major control on resistance variation as σz contains more site‐specific information like bed structure. The topography measurements for step‐pool channels should at least contain measurements on key roughness elements like steps. For gravel‐dune or plane‐bed channels, the proper resolution should be higher than 1/2 dune wavelength and 2D84, respectively. The choice of proper reach length relates to both R/k and roughness type. Further, hydraulic geometry functions with either D84 or σz as k are proposed, and the relation between the two metrics is discussed. Key Points The standard deviation of bed elevation σz more universally characterizes bed roughness k than D84 across a wide range of river conditions The Smart and Jäggi equation with σz as k outperforms others based on a large data set of 2,501 measurements under a wide range of conditions Accurate σz measurements require spatial resolution above 2D84 (plane‐bed), 0.5 dune wavelength (dune‐bed), and inter‐step spacing (step‐pool)